Statistics

Probing with low frequency electric currents.

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Author

Date

Permanent Link

Thesis Discipline

Electrical Engineering

Degree Grantor

University of Canterbury

Degree Level

Doctoral

Degree Name

Doctor of Philosophy

Four aspects of probing with low frequency electric currents are
considered.
Applications of probing with electric currents in geophysics and
medicine are reviewed. The theory of conservative fields is reviewed, and
is discussed in relation to low frequency electric currents and other
physical phenomena to which it applies.
The resolution with which a conductivity distribution can be reconstructed
from electrical measurements is examined. Relationships are
derived which relate the accuracy of the measurements to both the spatial
resolution and conductivity resolution of the distribution. These relationships
are obtained for conductivity distributions within both circular and
half plane regions. It is found that the spatial resolution and conductivity
resolution at any point depend on both the location and the conductivity
of that point. It is experimentally verified that the best theoretical
value of spatial resolution, for measurements having a particular
accuracy, can be closely approached in practice.
The relationship between two-dimensional circularly symmetric conductivity
distributions and electrical probing measurements performed on them is
studied. Two approaches are employed. One treats these distributions as
smooth and the other treats them as piecewise constant. Two techniques
are developed for reconstructing the conductivity distributions from the
measurements. One technique is iterative whereas the other is direct.
Examples are given in which these techniques are applied to a variety of
simulated and experimental measurements. These examples show how well
conductivity distributions, reconstructed by these techniques, can be
expected to represent the actual conductivity distributions.
The relationship between electrical probing measurements and general
two-dimensional conductivity distributions is examined. These distributions
are represented both as being smooth and piecewise continuous. Equations
are developed relating the measurements on the boundary of a region to the
conductivity distribution therein. The conditions on such measurements,
for them to fully characterise the electrical response of the region, are
established. The circumstances are identified under which coupling between different portions of the region can be neglected. These circumstances
are experimentally verified. A direct technique is developed for interpreting
measurements in terms of a particular type of conductivity distribution. This technique is applied successfully to both experimental and
simulated measurements.
A model is developed to interpret changes in limb volume measured
during venous occlusion plethysmography. The parameters of the model are
chosen to represent, as closely as possible, physiological variables of the
limb. Experiments are reported in which these changes in volume are infer
from measurements of the electrical resistance of limbs. It is shown that
the model can accurately mimic such changes in volume. An experiment is
described which demonstrates how changes in the model parameters can be USE
to monitor changes in the circulatory system within the limb. The model
used to show that significant changes in the limb circulation can occur
during surgery. Such changes have particular relevance to the formation c
peri-operative venous thrombosis.